## 9.3. Bernoulli, Johan (1667-1748)

Johann Bernoulli was one of the pioneers in the field of calculus and helped apply the new tool to real problems. His life was one of the most controversial of any mathematician. He was a member of the world's most successful mathematical family, the Bernoullis.Johann (also known as Johannes, Jean or John, depending on the translation) Bernoulli was born in Basel, Switzerland, on August 6, 1667. His family had originally been from Antwerp, Belgium, but had fled to avoid persecution by Catholics. After first settling down in Frankfurt, Johann's grandfather moved to Basel in 1622. Johann was the tenth son of a successful merchant and local official.

Originally, Johann's father had attempted to make a merchant out of his child but the son failed miserably as an apprentice. In 1683, he was given permission to enter the University of Basel, where his older brother Jacob, who was also a great mathematician, was already a professor. While pursuing a degree in medicine, Johann was tutored in mathematics by his older brother and soon developed a mastery of the new Leibnizian calculus. In 1694, he had committed himself to this new field and received his doctorate on a mathematical paper on muscular movement.

Unable to get the seat of mathematics at University of Basel because his brother held it, Johann accepted a position at the University of Groningen. In 1705, he returned to Basel after his brother's death to take Jacob's old position at the university. During his life he was awarded many honors including membership at the Academies of Science at Paris, Berlin, St. Petersburg and many others. He died in Basel on January 1, 1748.

Johann's life was always full of controversy. His first conflict occurred in 1691 on a visit to Paris. There he met France's leading mathematician L'Hospital, who persuaded him to teach him the calculus. For a fee, Bernoulli gladly complied and corresponded afterwards. However, the friendship died suddenly when L'Hospital published a textbook on differential calculus. Everything in the book was from Johann's notes and letters but the Frenchman claimed it as his own original work. Bernoulli was obviously enraged by the theft and ceased helping his freeloading friend.

Family troubles soon took over his attention. The relationship with his brother Jacob crumbled. After educating his brother in calculus, Jacob just could not accept his brother as his equal mathematically. After Johann solved a complicated problem before his brother, Jacob referred to him as "his pupil" and stated all of Johann achievements could be linked back to his teacher. Johann detested this belittling and the two engaged in public criticism of each other's work. At times, the letters became rather heated as insults seemed just as important as the mathematical problem being discussed. Curiously, however, the two seemed to develop ideas building off the other brother's work and in many cases it is likely the two at least collaborated on several occasions.

The family problems did not end there. In 1700, his son Daniel was born. Daniel, who would later become famous in physics for the founding of hydrodynamics, did not have a good relationship with his father. It appears Johann was jealous of his son. In one incident, Daniel was kicked out of the house for winning a prize that both of them had competed for. In an even more horrible, not to mention dishonest, display, Johann wanted credit for a discovery his son had made. In a flagrant case of plagiarism, he stole one of his son's papers, changed the name and date and claimed it as his own. These incidents were only two of many atrocious deeds committed by Johann against his son.

Finally, Bernoulli also became engaged in the mathematical dispute of his day. Having learned Leibnizian calculus, he began a correspondence with Leibniz himself. In 1713, with the dispute over who invented calculus between Leibniz and Newton in full swing, Bernoulli took the side of his friend. Because of his support, Leibniz's calculus gained preference in continental Europe.

When not engaged in some dispute or another, Johann had many discoveries in the field of calculus. He
and his brother Jacob are credited with the beginnings of the calculus of variations, which was inspired
over an argument on a geometric figure known as the brachistochrone. The two brothers also discovered
many new applications for the new calculus which spread its popularity. Johann himself did important
work on the study of the equation *y = x ^{x}*, discovered the
Bernoulli series and made
advances in theory of navigation and ship sailing. In addition, he is famous for his tremendous letter
writing (over 2500 messages) and his tutoring of another great mathematician, Leonhard Euler.

As for the rest of the Bernoulli family, there were eight good mathematicians over three generations. The three most significant were Jacob, Johann and Daniel who have already been mentioned. However, also of importance were Johann's brother Nikolaus, Johann's sons Nikolaus and Johann II, and his grandsons Johann III and Jacob.

For related information on Bernoulli, see: Leonhard Euler , Bernoulli's inequality.

**Sources**

- Abbott, David Ph.D. ed. "Bernoulli, Jacques & Bernoulli, Jean."
*The Biographical Dictionary of Sciences: Mathematics*. New York: Peter Bedrick Books, 1985. p. 17. - Bell, E.T.
*Men of Mathematics.*New York: Simon and Schuster, Inc., 1937. - Fellman, E. A. & J. O. Fleckenstein. "Bernoulli, Johann (Jean) I."
*Dictionary of Scientific Biography*. New York: Charles Scribner's Sons, 1970. vol. 1, pp. 51-55. - Sensenbaugh, Roger. "The Bernoulli Family."
*Great Lives from History Renaissance to 1900 Series*. Englewood Cliffs, NJ: Salem Press, 1989. vol. 1, pp. 185-188.

**Paul Golba**